Factor analysis by generalized least squares

Aitken's generalized least squares (GLS) principle, with the inverse of the observed variance-covariance matrix as a weight matrix, is applied to estimate the factor analysis model in the exploratory (unrestricted) case. It is shown that the GLS estimates are seale free and asymptotically efficient. The estimates are computed by a rapidly converging Newton-Raphson procedure. A new technique is used to deal with Heywood cases effectively.The work on this project was done when the first author was Research Statistician at Educational Testing Service, Princeton, N. J. The second author was in part supported by a grant from the Research Committee of the University of Wisconsin Graduate School. The authors wish to thank Michael Browne for many helpful comments and Marielle van Thillo for valuable assistance in the numerical computations.     

An individual difference model for the multidimensional analysis of preference data

A model for the analysis of paired comparison data is presented which combines features of the BTL-model with features of the Unfolding model. The model is metric, mathematically tractable, and has an exact algebraic solution. Since it is multidimensional and allows for individual differences, it is thought to be more realistic for some choice situations than either the Thurstone model or the BTL-model. No claim is made that the present model will be appropriate for all conceivable choice situations. Rather, it is argued that the fact that it is explicitly falsifiable is a point in its favor.This work was supported by a grant of the United States Public Health Service (1 R03 MH19139 01 MSM) and a David Ross (XR) grant of the Purdue Research Foundation (PRF 2132), both of which are gratefully acknowledged. We also owe thanks to Dr. Terry Cooper, whose careful scrutiny of an earlier draft of this paper allowed us to reduce the number of errors from n to n-1.     

Some new results on factor indeterminacy

Some relations between maximum likelihood factor analysis and factor indeterminacy are discussed. Bounds are derived for the minimum average correlation between equivalent sets of correlated factors which depend on the latent roots of the factor intercorrelation matrix . Empirical examples are presented to illustrate some of the theory and indicate the extent to which it can be expected to be relevant in practice.     

The effect of memory load on reaction time in character classification

In order to investigate the effect of memory load on reaction time (RT), choice RT trials were embedded in a binary character classification task using the varied set procedure. Twelve Ss performed in experimental blocks, as well as in control blocks consisting of character classification trials only. In experimental blocks, every trial began as a classification trial with the presentation of a new positive set. On a random half of these trials, however, a choice RT stimulus was presented instead of a probe letter and S simply made the indicated response. Results indicated that memory load had no effect on the choice RT trials. Embedding choice RT trials in the classification task affected the intercept (but not the slope) of the function relating classification RT to memory load. This result implies that the increase in latency usually obtained in classification experiments is entirely due to an increase in the duration of the memory searching stage of processing.     

Cross-task validation of functional measurement

Ss judged average heaviness of two unseen lifted weights on a 20-step rating scale. They also rated heaviness of a single visible object of variable size and weight. The data for each task obeyed the parallelism prediction of the linear integration model. This within-task consistency validates jointly the model and the response scale. Functional measurement procedure yielded independent scales of subjective heaviness from each task. These were linearly related, a criterion of external consistency. The plot of subjective heaviness against objective weight was slightly negatively accelerated. These results disagree with those that have been obtained with magnitude estimation. Since the rating data satisfy both internal and external consistency, they constitute the true measure of sensation. Magnitude estimation, in contrast, must be biased and invalid.